The DOI matches its Crossref record; 50 of the 50 references it cites were found in a registry or an index; 3 of the 11 sources its claims cite were checked for support.
Strain-induced pseudomagnetic field and photonic Landau levels in dielectric structures
Open accessAbstract
By properly structuring a dielectric lattice, it is possible to induce a pseudomagnetic field at optical frequencies in a photonic lattice, where the propagation dynamics is equivalent to the evolution of an electronic wavepacket in graphene.
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29 Own interpretation · 25 No basis given · 20 Own result · 8 No full text of the sources · 3 Couldn’t confirm · accuracy not yet measured
The cited sources that could be checked couldn’t confirm or dispute this claim.
In the paper
“It has been shown for graphene that for wavepackets that lie near a Dirac point, straining the system is mathematically equivalent to introducing magnetic fields 3 .”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Abstract
What the sources say
- Could not verifycites [3] Hafezi, M., Demler, E. A., Lukin, M. D. & Taylor, J. M. Robust optical delay lines with topological protection. Nature Phys. 7, 907–912 (2011). sourceExperimental — accuracy not yet measured
The 2D Photonic System and Quantum Spin Hall Hamiltonian section (pp. 1–3) describes synthetic magnetic fields produced by phases in coupled optical resonators, not by straining graphene. Searches for graphene, strain, and Dirac points found no passage addressing the claimed equivalence for wavepackets near a Dirac point. (LLM, conf=0.76)
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In the paper
“€ β = ±ω N € N = 0,1,2,... € ω = 3 Bc 0 a /2”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Abstract
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In the paper
“We show experimentally and numerically that the gaps between these Landau levels give rise to transverse confinement of the optical modes.”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Abstract
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In the paper
“In the present work, we demonstrate the existence of pseudomagnetism in such photonic lattices by virtue of the inhomogeneous strain.”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Abstract
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In the paper
“Here, we show experimentally and theoretically that, by properly structuring a dielectric lattice, it is possible to induce a pseudomagnetic field at optical frequencies in a photonic lattice, where the propagation dynamics is equivalent to the evolution of an electronic wavepacket in graphene.”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Abstract
boosteddirect- Asserted: passes — The authors put it forward as true.
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In the paper
“Note that the numerically calculated positions of the Landau levels coincide exactly with the analytically predicted values (which assume that the states at the vicinity of the Dirac point obey the Dirac equation).”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Abstract
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- The authors state this as an assumption: The states at the vicinity of the Dirac point obey the Dirac equation.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The induced field gives rise to multiple photonic Landau levels (singularities in the density of states) separated by band gaps.”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Abstract
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In the paper
“Furthermore, the strain introduces edge states that are normally associated with the zig-zag and bearded edges 31 at .”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Abstract
What the sources say
- Not checked — no full text of the sourcecites [31] Kohmoto, M. & Hasegawa, Y. Zero modes and edge states of the honeycomb lattice. Phys. Rev. B 76, 205402 (2007). source
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“As a result, some of the Landau level eigenstates have significant power residing on the armchair edges of the sample.”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Abstract
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“In the paper, we claim that by launching light in a single waveguide on the armchair edge of the strained photonic lattice, we only excite modes within the Dirac region.”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Section 3: Coupled-mode theory analysis: exciting single waveguides on armchair edge excites modes entirely within the Dirac region
plaindirect- Asserted: passes — The authors put it forward as true.
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- The authors state this as an assumption: In coupled-mode theory, the continuum wavefunction ψ(x,y,z) can be written as the sum of waveguide modes centered on each waveguide.
- Probably not a substantial claim. 7
- It may state two separate claims as one. 21
- The quote only partly states this claim. 3
The cited sources that could be checked couldn’t confirm or dispute this claim.
In the paper
“In graphene, however, it has been shown that inhomogeneous strains can induce 'pseudomagnetic fields' that behave very similarly to real fields 3 .”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Abstract
What the sources say
- Could not verifycites [3] Hafezi, M., Demler, E. A., Lukin, M. D. & Taylor, J. M. Robust optical delay lines with topological protection. Nature Phys. 7, 907–912 (2011). sourceExperimental — accuracy not yet measured
The 2D Photonic System and Quantum Spin Hall Hamiltonian section (pp. 1, 3) describes synthetic magnetic fields in coupled optical resonators. Searches for graphene, inhomogeneous strain, and strain-induced pseudomagnetic fields found no passage in our copy addressing the claim. (LLM, conf=0.76)
plaindirect- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim.
- Could not verify
The cited sources that could be checked couldn’t confirm or dispute this claim.
In the paper
“More than a decade ago, Kane and Mele 3 showed that inhomogeneously strained graphene (a honeycomb lattice of carbon atoms) results in similar physical behavior as adding an external magnetic field.”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Abstract
What the sources say
- Could not verifycites [3] Hafezi, M., Demler, E. A., Lukin, M. D. & Taylor, J. M. Robust optical delay lines with topological protection. Nature Phys. 7, 907–912 (2011). sourceExperimental — accuracy not yet measured
The 2D Photonic System and Quantum Spin Hall Hamiltonian section (pp. 1, 3) describes synthetic magnetic fields in coupled optical resonators, not strain in graphene. Searches for Kane and Mele, inhomogeneously strained graphene, and strain-induced magnetic behavior found no passage in our copy addressing the attributed claim. (LLM, conf=0.76)
plaincorrelational- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim.
- Could not verify
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The unstrained system has only armchair-type edges, no zig-zag or bearded edges.”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Abstract
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“When the system is properly strained, the states within the Dirac cone split up into highly degenerate Landau levels, with band gaps lying in between them (Fig. 2b).”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“In Fig. 2d, we see that the strain clearly induces kinks in the spectrum that correspond to values of the propagation constant in which many eigenstates reside: these are the Landau levels; their propagation constants may be calculated, as described above, to be .”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Abstract
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In the paper
“The states in between the levels are localized solely on the edges of the lattice, i.e., these are strictly edge states that are not present in the limit of infinite system size.”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Abstract
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In the paper
“As was mentioned previously, the strained armchair edge does have edge states associated with it, all lying at propagation constant 31 , like the zig-zag and bearded edge states.”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Abstract
What the sources say
- Not checked — no full text of the sourcecites [31] Kohmoto, M. & Hasegawa, Y. Zero modes and edge states of the honeycomb lattice. Phys. Rev. B 76, 205402 (2007). source
plaincorrelational- Asserted: passes — The authors put it forward as true.
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The quote only partly states this claim.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“in the present work the waveguides are designed to be singlemoded”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Section 2: Calculating guided eigenmodes of femtosecond-written waveguides
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Probably not a substantial claim. The paper may give no reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Note that despite the anisotropy of the waveguide itself, the mode associated with the waveguide is quite isotropic and so the anisotropy of the coupling is negligible.”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Section 2: Calculating guided eigenmodes of femtosecond-written waveguides
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds. It may state two separate claims as one.
- The authors state this as an assumption: In coupled-mode theory, the continuum wavefunction ψ(x,y,z) can be written as the sum of waveguide modes centered on each waveguide.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Note that the first and second bands intersect at the Dirac cones (one of which is indicated by an arrow), which reside at the vertices of the Brillouin zone.”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Abstract
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“For sufficiently large strain, light is confined to the edge when the states excited are in a bulk band gap, and thus the light attempting to tunnel from the excited edge waveguide cannot penetrate into the bulk.”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Abstract
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In the paper
“(f) A stronger positive defect (! !/! != 2) causes greater spreading (as in (d)) as a result of strong coupling to the bulk bands.”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Abstract
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In the paper
“Clear Landau levels emerge in the spectrum as a result of the strain (labeled 'LL'), with edge states lying in between them.”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Abstract
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In this way, we obtain a value of c 0 = 1.9×10 !! !! !! .”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Section 2: Calculating guided eigenmodes of femtosecond-written waveguides
plain- Asserted: passes — The authors put it forward as true.
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The quote only partly states this claim.
- The authors state this as an assumption: In coupled-mode theory, the continuum wavefunction ψ(x,y,z) can be written as the sum of waveguide modes centered on each waveguide.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The spatial spectrum of the eigenmodes is shown in blue as a guide to the eye of where the Landau levels (as well as the edge states in between them) reside.”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Section 3: Coupled-mode theory analysis: exciting single waveguides on armchair edge excites modes entirely within the Dirac region
plaincorrelational- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“As the degree of strain, q, is increased, the light becomes more and more localized on the armchair edge, remaining largely within the same waveguide where it was launched (right column, middle and bottom rows).”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Abstract
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“unlike what is happening in an unstrained lattice -where light launched into a defect waveguide remains in that waveguide throughout propagation”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Section 2: Calculating guided eigenmodes of femtosecond-written waveguides
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper may give no reason why it holds.
- The authors state this as an assumption: In coupled-mode theory, the continuum wavefunction ψ(x,y,z) can be written as the sum of waveguide modes centered on each waveguide.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The pseudomagnetism, while not breaking timereversal symmetry, leads to the generation of discrete Landau levels in the spatial spectrum, which are impossible in a periodic structure.”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Abstract
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In the paper
“Note that this is an accurate description of the band structure only in the Dirac regions.Outside the Dirac regions, the eigenstates form a continuous band and cannot be described by the pseudomagnetic field.”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Abstract
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In the paper
“This is because half of the Dirac cones exhibit pseudomagnetic fields in the +z direction, while the other half are in the -z direction 23 .”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Abstract
What the sources say
- Not checked — no full text of the sourcecites [23] Malkova, N., Hromada, I., Wang, X., Bryant, G. & Chen, Z. Observation of optical Shockley-like surface states in photonic superlattices. Opt. Lett. 34, 1633–1635 (2009). source
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“By choosing a particular form of the strain tensor , it was demonstrated in graphene 10 that a vector potential corresponding to a constant magnetic field could be achieved, along with a total absence of electric field.”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Abstract
What the sources say
- Not checked — no full text of the sourcecites [10] Bahat-Treidel, O., Peleg, O. & Segev, M. Symmetry breaking in honeycomb photonic lattices. Opt. Lett. 33, 2251–2253 (2008). source
boosteddirect- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“If a piece of graphene were strained to this extent, it would yield a magnetic field of 5500T.”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Abstract
hedgeddirect- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Note that the induced pseudomagnetic field does not break z-reversal invariance, just like a pseudomagnetic field in atomic graphene does not break time-reversal symmetry.”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Abstract
plain- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In contradistinction with these, the structure we propose here -a strained honeycomb photonic lattice --contains no metals and is non-resonant, and is therefore loss-free.”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The spacing of these Landau levels is unique to honeycomb structures, and is strongly affected by the conical dispersion at the vicinity of the Dirac cones.”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Abstract
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In summary, the strain leads to confinement for two reasons: (1) the initial beam excites states in the gap between Landau levels, which are confined to the edge; and (2) the initial beams excite degenerate edge states in the zeroth Landau level which cannot cause diffraction due to their degeneracy.”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“Outside the band, the state resides in a band gap (although not one induced by the strain), and thus cannot overlap with any modes that spread throughout the bulk of the photonic lattice.”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Therefore, despite the fact that these edge states are degenerate with the zeroth Landau level and are resonantly coupled to bulk states, they do not couple into the bulk, and the light is therefore confined on the edge.”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“As described in the text, this results from the fact that the eigenstates excited by the incoming light are either in a band gap between Landau levels (and therefore cannot penetrate into the bulk), or are degenerate states in the zeroth Landau level, also resulting in edge confinement.”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
The authors state this as an assumption.
In Eq. (1), the waveguides are sufficiently distant from one another that only nearest-neighbor coupling needs to be incorporated.
“For simplicity, in Eq. ( 1) we assume that the waveguides are sufficiently distant from one another, such that it is only necessary to incorporate nearestneighbor coupling.”
The authors state this as an assumption.
Each of the waveguides supports only a single mode.
“Furthermore, it is assumed that each of the waveguides supports only a single mode.”
The authors state this as an assumption.
The states at the vicinity of the Dirac point obey the Dirac equation.
“Note that the numerically calculated positions of the Landau levels coincide exactly with the analytically predicted values (which assume that the states at the vicinity of the Dirac point obey the Dirac equation).”
The paper relies on this without support.
The armchair edge has no edge states.
“This waveguide resides at the armchair edge, which has no edge states.”
“Due to the lack of edge states on the armchair edge, no light is confined to the edge and it diffracts into the bulk.”
The authors state this as an assumption.
The dielectric structure of the femtosecond-written waveguides can be described by a hypergaussian function.
“Its dielectric structure can be described as a hypergaussian function:”
The authors state this as an assumption.
In coupled-mode theory, the continuum wavefunction ψ(x,y,z) can be written as the sum of waveguide modes centered on each waveguide.
“In coupled-mode theory, we assume that the continuum wavefunction !!, !, !can be written as the sum of waveguide modes centered on each waveguide.”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“This was observed in numerical tight-binding calculations and experimentally via the localization of a wave packet on the edge of a strained lattice (Rechtsman, Zeuner, Tünnermann et al., 2013), attesting to both the presence of flat Landau bands and states localized at the edge emerging from the gauge field.”
From Topological photonics (2019) · cites this paper as Rechtsman, Zeuner, Tünnermann et al., 2013
Experimental — accuracy not yet measuredThe cited source says what the claim attributes to it.
In the citing paper
“We note that our vortex generation and topological charge flipping is achieved by exciting the two sublattices at the same K valley (see Fig. 3) in a uniform (non-strained) HCL, thus no pseudomagnetic field is involved 22 .”
From Unveiling pseudospin and angular momentum in photonic graphene (2015) · cites this paper as [22]
The cited source says what the claim attributes to it.
In the citing paper
“Recently, varieties of artificial systems have enabled the imitation and exploration of graphene and Dirac cones using the honeycomb structure with controllable parameters and observables [10-25] beyond traditional graphene itself where those are not easily accessible.”
From Observing movement of Dirac cones from single-photon dynamics (2021) · cites this paper as [14]
The cited source says what the claim attributes to it.
In the citing paper
“This precise idea was implemented by Rechtsman, Zeuner, Tünnermann et al. (2013) in a lattice of coupled waveguides by continuously varying their separation (i.e., the nearestneighbor photon hopping) following the above-mentioned strain configuration.”
From Topological photonics (2019) · cites this paper as Rechtsman, Zeuner, Tünnermann et al. (2013)
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Abstract
“we plot the values of (i.e., the spatial spectrum) in the Dirac region for an unstrained and a strained lattice, in descending order, in Figs.2c and 2d.”
§ Strain-induced pseudomagnetic field and Landau levels in photonic structures > Abstract
“(c) The numerically-computed eigenvalues plotted in ascending order in the region near the Dirac point for the unstrained lattice.”
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Cited by
Sorted by citations
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Metadata
- Authors
- Rechtsman, M. C., Zeuner, J. M., Tünnermann, A., Nolte, S., Segev, M., & Szameit, A.
- Affiliations
- Technion – Israel Institute of Technology (IL)
- Friedrich Schiller University Jena (DE)
- Corresponding author
- Rechtsman, Mikael C.
- Venue
- Nature Photonics
- Published
- 2012-12-09
- Volume
- 7
- Issue
- 2
- Pages
- 153-158
- ISSN
- 1749-4885 (ISSN-L)
- 1749-4893
- OpenAlex
- W2071086979
- Cited by
- 453
- References
- 47
- Citations by year
- 2026: 23 · 2025: 36 · 2024: 35 · 2023: 32 · 2022: 25 · 2021: 42 · 2020: 38 · 2019: 34 · 2018: 26 · 2017: 38 · 2016: 35 · 2015: 43 · 2014: 25 · 2013: 21
- FWCI
- 14.70
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Nature Photonics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Publikationsdatenbank der Fraunhofer-Gesellschaft (Fraunhofer-Gesellschaft) (submittedVersion, other-oa)
- Publikationsdatenbank der Fraunhofer-Gesellschaft (Fraunhofer-Gesellschaft) (submittedVersion)
- Fraunhofer-Publica (Fraunhofer-Gesellschaft) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Photonic Crystals and Applications
- Physical Sciences › Materials Science › Electronic, Optical and Magnetic Materials › Metamaterials and Metasurfaces Applications
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Topological Materials and Phenomena
- Keywords
- photonic crystals, strain heterogeneity, slow light, field enhancement, magneto-optical effect, density of states
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